[數學]卜瓦松分配

(a) A Poisson distribution makes the following assumptions:
1) Events must be independent of each other, i.e. occurrence of A does not alter the probability that B occurs.
2) We can always divide the "time line" of events in such a way that any segment contains no more than one occurrence. For example, in counting the number of accidents on a highway over a period of time, we assume that we can divide time into very fine segment (e.g. 1 nanosecond) such that no two accidents occur in that any 1 nanosecond interval.
3) Probability must increase as the interval concerned is made wider.

(b) λ= nθ= 2 per 30 seconds.
P(X = 4) = Poisson(4, 2) = 24*e-2/4! = 0.0902 or 9.02%.

(c) P(X < 3)
= Poisson(0,2)+Poisson(1,2)+Poisson(2,2)
= 20*e-2/0! + 21*e-2/1! + 22*e-2/2!
= 5e-2
= 0.6767 or 67.67%.

Hope this helps!

http://en.wikipedia.org/wiki/Poisson_distribution